Flavor-phenomenology of two-Higgs-doublet models with generic Yukawa structure

Abstract

In this article, we perform an extensive study of flavor observables in a two-Higgs-doublet model with generic Yukawa structure (of type III). This model is interesting not only because it is the decoupling limit of the minimal supersymmetric standard model but also because of its rich flavor phenomenology which also allows for sizable effects not only in flavor-changing neutral-current (FCNC) processes but also in tauonic $B$ decays. We examine the possible effects in flavor physics and constrain the model both from tree-level processes and from loop observables. The free parameters of the model are the heavy Higgs mass, $\mathrm{tan}\ensuremath{\beta}$ (the ratio of vacuum expectation values) and the ``nonholomorphic'' Yukawa couplings ${ϵ}_{ij}^{f}(f=u,d,\ensuremath{\ell})$. In our analysis we constrain the elements ${ϵ}_{ij}^{f}$ in various ways: In a first step we give order of magnitude constraints on ${ϵ}_{ij}^{f}$ from 't Hooft's naturalness criterion, finding that all ${ϵ}_{ij}^{f}$ must be rather small unless the third generation is involved. In a second step, we constrain the Yukawa structure of the type-III two-Higgs-doublet model from tree-level FCNC processes (${B}_{s,d}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, ${K}_{L}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, ${\overline{D}}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, $\ensuremath{\Delta}F=2$ processes, ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ and ${\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}}$) and observe that all flavor off-diagonal elements of these couplings, except ${ϵ}_{32,31}^{u}$ and ${ϵ}_{23,13}^{u}$, must be very small in order to satisfy the current experimental bounds. In a third step, we consider Higgs mediated loop contributions to FCNC processes [$b\ensuremath{\rightarrow}s(d)\ensuremath{\gamma}$, ${B}_{s,d}$ mixing, $K\ensuremath{-}\overline{K}$ mixing and $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$] finding that also ${ϵ}_{13}^{u}$ and ${ϵ}_{23}^{u}$ must be very small, while the bounds on ${ϵ}_{31}^{u}$ and ${ϵ}_{32}^{u}$ are especially weak. Furthermore, considering the constraints from electric dipole moments we obtain constrains on some parameters ${ϵ}_{ij}^{u,\ensuremath{\ell}}$. Taking into account the constraints from FCNC processes we study the size of possible effects in the tauonic $B$ decays ($B\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\nu}$, $B\ensuremath{\rightarrow}D\ensuremath{\tau}\ensuremath{\nu}$ and $B\ensuremath{\rightarrow}{D}^{*}\ensuremath{\tau}\ensuremath{\nu}$) as well as in ${D}_{(s)}\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\nu}$, ${D}_{(s)}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\nu}$, $K(\ensuremath{\pi})\ensuremath{\rightarrow}e\ensuremath{\nu}$, $K(\ensuremath{\pi})\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\nu}$ and $\ensuremath{\tau}\ensuremath{\rightarrow}K(\ensuremath{\pi})\ensuremath{\nu}$ which are all sensitive to tree-level charged Higgs exchange. Interestingly, the unconstrained ${ϵ}_{32,31}^{u}$ are just the elements which directly enter the branching ratios for $B\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\nu}$, $B\ensuremath{\rightarrow}D\ensuremath{\tau}\ensuremath{\nu}$ and $B\ensuremath{\rightarrow}{D}^{*}\ensuremath{\tau}\ensuremath{\nu}$. We show that they can explain the deviations from the SM predictions in these processes without fine-tuning. Furthermore, $B\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\nu}$, $B\ensuremath{\rightarrow}D\ensuremath{\tau}\ensuremath{\nu}$ and $B\ensuremath{\rightarrow}{D}^{*}\ensuremath{\tau}\ensuremath{\nu}$ can even be explained simultaneously. Finally, we give upper limits on the branching ratios of the lepton flavor-violating neutral $B$ meson decays (${B}_{s,d}\ensuremath{\rightarrow}\ensuremath{\mu}e$, ${B}_{s,d}\ensuremath{\rightarrow}\ensuremath{\tau}e$ and ${B}_{s,d}\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\mu}$) and correlate the radiative lepton decays ($\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$, $\ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ and $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$) to the corresponding neutral current lepton decays (${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ and ${\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}}$). A detailed Appendix contains all relevant information for the considered processes for general scalar-fermion-fermion couplings.